CLˆOTURE INTÉGRALE DES IDÉAUX ETÉQUISINGULARITÉ

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[G3] T. Gaffney, Multiplicities and equisingularity of ICIS germs, Inventiones Math., 123 (1996), 209-220. [G4] T. Gaffney,The theory of integral closure of ideals and modules: applications and new developments With an appendix by Steven Kleiman and Anders Thorup. NATO Sci. Ser. II Math. Phys. Chem., 21, New developments in singularity theory (Cambridge, 2000), 379–404, Kluwer Acad. Publ., Dordrecht, 2001. [Ge] Murray Gerstenhaber, On the deformation of rings and algebras, II. Ann. of Math. 84 (1966), 1-19. [Gw] Janusz Gwo´zdziewicz, The Lojasiewicz exponent at an isolated zero, Commentarii Math. Helvetici, 74, (1999), 364-375. [G-K 1] T. Gaffney, Steven L. Kleiman, Specialization of integral dependence for modules, Inv. Math., 137 (1999), no. 3, 541-574. [G-K 2] T. Gaffney, S. Kleiman, Wf and integral dependence, Real and Complex singularities (Sao Carlos, 1998) Chapman and Hall//CRC Res. Notes in Math., 412, 33-45, Chapman and Hall//CRC Boca Raton, Florida, 2000. [GB] Evelia García Barroso, Sur les courbes polaires d’une courbe plane réduite, Proc. London Math. Soc. (3) 81 (2000) 1-28. [GB-G] E. García Barroso, Janusz Gwo´zdziewicz, Characterization of jacobian Newton polygons of branches, Manuscrit, 2007. [GB-P] E. García Barroso, Arkadiusz P̷loski, On the ̷Lojasiewicz numbers, C. R. Acad. Sci. Paris, Ser. I., 336 (2003), 585-588. [GB-K-P 1] E. García Barroso, Tadeusz Krasiński, A. P̷loski, On the ̷Lojasiewicz numbers, II, C. R. Acad. Sci. Paris, Ser. I., 341 (2005), 357-360. [GB-K-P 2] E. García Barroso, T. Krasiński, A. P̷loski, The ̷Lojasiewicz numbers and plane curve singularities, Ann. Pol. Math., 87 (2005), 127-150. [G-T] Rebecca Goldin, B. Teissier, Resolving plane branch singularities with one toric morphism, in “Resolution of Singularities, a research textbook in tribute to Oscar Zariski”, Birkhäuser, Progress in Math. No. 18 (2000), 315-340. [H] Gordon Heier, Finite type and the effective Nullstellensatz, ArXiv: Math/AG 0603666. [Hi] Michel Hickel, Solution d’une conjecture de C. Berenstein-A. Yger et invariants de contact à l’infini, Ann. Inst. Fourier (Grenoble), 51, No.3 (2001), 707-744. [Hu] Craig Huneke, Tight closure and its applications, C.B.M.S. Lecture Notes 88 74
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hal-00261772, version 1 - 16 Mar 20
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the monomial curve corresponding to
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0.1.3. Remarques. — Si µ est une
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0.1.10. — De même si J est un id
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Soit k0 = mk ′ 0 et posons N = su
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Z Soit ν(n) = νI ′(J ′n ) J n
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Réciproquement, soit (fT) k + b1(f
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En effet d’une part ii’) entra
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total de fractions n’est donc rie
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2.1. Théorème. — Soient X un es
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méromorphe et bornée serait holom
Page 23 and 24: un nombre fini d’ouverts Vα rela
Page 25 and 26: Démonstration. — C’est la clô
Page 27 and 28: Or, tensorisons (∗) au-dessus de
Page 29 and 30: Démonstration. — Soit C le condu
Page 31 and 32: 4.1. Calcul de ¯ν dans l’éclat
Page 33 and 34: tout f ∈ Γ(V, OX), on ait ¯ν K
Page 35 and 36: 4.2. Définition des I p/q . 4.2.1.
Page 37 and 38: Démonstration. — Soient U un ouv
Page 39 and 40: et v ϕ(aj) ≥ j p q v ϕ(I) o
Page 41 and 42: 4.4.0. — Nous allons maintenant u
Page 43 and 44: f ∈ O tel que ¯νI(f) = 0, l’i
Page 45 and 46: [d − ε, d + ε]. Le même raison
Page 47 and 48: et le critère valuatif de dépenda
Page 49 and 50: 5.7. — Un cas où l’on peut cal
Page 51 and 52: Si l’ensemble de ces θ est vide,
Page 53 and 54: 2) ¯ν K I (f) = inf x∈K ¯νx p
Page 55 and 56: Dans ce cas l’anneau O = OX,x ⊗
Page 57 and 58: est par hypothèse un idéal réel
Page 59 and 60: et montré que si K est sous-analyt
Page 61 and 62: fO X ′ ∈ ĨO X ′ à cause de
Page 63 and 64: par les ( ∂f ∂z1 ◦ π, . . .
Page 65 and 66: ment irréductibles X j(i) du germe
Page 67 and 68: montre en particulier que le polygo
Page 69 and 70: estimées hypoelliptiques, dont on
Page 71 and 72: l’inégalité T(I) ≤ (L n ). Ap
Page 73: BIBLIOGRAPHIE [Bö1] Erwin Böger,
Page 77 and 78: 6 (1956), 161-174. [R2] D. Rees, va
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